Well, Amazon and MSFT will not provide offers for new grads that will even match the entry level Google offer. So that leaves FB who isn't paying new grads as much as they used to. There aren't too many companies that will give offers that will allow you to negotiate to 250 which is really high.
Some junior engineers do (most don't). There was this thread from a while ago [0] where someone negotiated a 300k offer. I believe they were a new/recent grad.
Most of the time it's due to having some leverage (multiple FAANG+ offers).
L4 to L5 is no cakewalk. you have to be rock solid in the core SWE disciplines and have excellent communication, organization skills, and very good leadership skills too. looking at the stats, promoted as a % of total for L4 to L5 just makes it into the double digits and only a little over a quarter of all SWEs are L5.
the SWE ladder requires/expects for an L3 to get to L4 by makes no such requirement to ever get to L5.
That is why you don't play the promo game and get promoted via interviews at other companies. When you reach staff, that is usually when you have to practically start playing promo games. Not everywhere is google with their slow promo processes.
Also career and personal skill wise, it's good to see how other companies work. Pay is in many ways determined by your negotiation skills, and that is empowered by creating better BATNAs via interview skill.